Evaluate 2 square root of 3( square root of 8-5 square root of 6)

Solve Math

Trigonometry

$2 \sqrt{3} (\sqrt{8} - 5 \sqrt{6})$

Simplify each term.

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Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$2 \sqrt{3} (\sqrt{4 (2)} - 5 \sqrt{6})$

Rewrite $4$ as $2^{2}$ .

$2 \sqrt{3} (\sqrt{2^{2} \cdot 2} - 5 \sqrt{6})$

Pull terms out from under the radical.

$2 \sqrt{3} (2 \sqrt{2} - 5 \sqrt{6})$

Apply the distributive property.

$2 \sqrt{3} (2 \sqrt{2}) + 2 \sqrt{3} (- 5 \sqrt{6})$

Multiply $2 \sqrt{3} (2 \sqrt{2})$ .

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Multiply $2$ by $2$ .

$4 \sqrt{3} \sqrt{2} + 2 \sqrt{3} (- 5 \sqrt{6})$

Combine using the product rule for radicals.

$4 \sqrt{2 \cdot 3} + 2 \sqrt{3} (- 5 \sqrt{6})$

Multiply $2$ by $3$ .

$4 \sqrt{6} + 2 \sqrt{3} (- 5 \sqrt{6})$

Multiply $2 \sqrt{3} (- 5 \sqrt{6})$ .

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Multiply $- 5$ by $2$ .

$4 \sqrt{6} - 10 \sqrt{3} \sqrt{6}$

Combine using the product rule for radicals.

$4 \sqrt{6} - 10 \sqrt{6 \cdot 3}$

Multiply $6$ by $3$ .

$4 \sqrt{6} - 10 \sqrt{18}$

Simplify each term.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$4 \sqrt{6} - 10 \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{6} - 10 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt{6} - 10 (3 \sqrt{2})$

Multiply $3$ by $- 10$ .

$4 \sqrt{6} - 30 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{6} - 30 \sqrt{2}$

Decimal Form:

$- 32.62844790 \dots$

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Name

Name	one billion four hundred eighty-nine million six hundred fourteen thousand one hundred sixty-six

Interesting facts

1489614166 has 4 divisors, whose sum is 2234421252
The reverse of 1489614166 is 6614169841
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 46
Digital Root 1

Name

Name	seven hundred fifty-one million seven hundred four thousand two hundred twenty-one

Interesting facts

751704221 has 8 divisors, whose sum is 759475200
The reverse of 751704221 is 122407157
Previous prime number is 991

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 29
Digital Root 2

Name

Name	four hundred seven million three hundred ten thousand eight hundred ninety-four

Interesting facts

407310894 has 8 divisors, whose sum is 678851520
The reverse of 407310894 is 498013704
Previous prime number is 9

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

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